Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…

In this note we show the existence of a surprising analogy between quadrilaterals and tetrahedra, determining some properties that hold for both families of figures. This analogy suggests some new properties of quadrilaterals. (Contains 11 figures,)

The butterfly curve was introduced by Temple H. Fay in 1989 and defined by the polar curve r = e[superscript cos theta] minus 2 cos 4 theta plus sin[superscript 5] (theta divided by 12). In this article, we develop the mathematical model of the butterfly curve and analyse its geometric properties. In addition, we draw the butterfly curve and…

Many undergraduate students have difficulty writing mathematical proofs even though this skill is important for the development of future teachers and those who may be involved in instruction or training as a graduate student or supervisor. In addition, research indicates that mathematics majors and secondary education mathematics majors possess…

We present a general formula for a triple product involving four real numbers. As a particular case, we get the sum of a triple product of four odd integers. Some interesting results are recovered. We derive a general formula for more than four odd numbers.

Mathematics and science are tightly interwoven, yet they are often treated as distinct disciplines in the educational context. This study details the development, implementation and outcomes of a teaching intervention that highlights the links between mathematics and science, in the form of a first-year interdisciplinary course. A mixed method…

Characteristic polynomials are used to determine when magic squares have magic inverses. A resulting method constructs arbitrary examples of such squares.

This note presents a teaching suggestion, using the history of mathematics, to give students from middle school and high school the possibility of facing problems found in old mathematics books and comparing their solutions with those given in those books. (Contains 3 figures and 1 table.)

In this note 4 x 4 most-perfect pandiagonal magic squares are considered in which rows, columns and the two main, along with the broken, diagonals add up to the same sum. It is shown that the Moore-Penrose inverse of these squares has the same magic property.

Inspiring exercises are used to guide students at all levels to rediscover the essential meaning of various individual pieces of mathematics. Presents five sets of examples including Abel's identity, Hensel's lemma, finitely generated Abelian groups, Baire's category theorem, and the Weierstrass preparation theorem. (Author/ASK)

Integrates different geometries and blends several topics that have important applications in both higher mathematics and other disciplines. Aims to make these topics more attractive and understandable to high school students in a way that reinforces logical thinking with visual understanding obtained through computer usage. Contains 28…

Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Describes an exploration into the concept of the rate of convergence in a university classroom. It is well known in mathematics that this concept leads to a modern construction of infinitesimals and their orders. (Author)

Describes a process for creating a more diverse set of experiences for undergraduate students in mathematics by focusing on linear algebra. Emphasizes that the diversity of the activities is generated in part through the use of a taxonomy that addresses the nature of the activities rather than a hierarchy of levels of difficulty. Contains 13…